question 5 (multiple choice worth 3 points)
(simple interest and arithmetic sequences mc)

an auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?

60
93
102
110

Question

question 5 (multiple choice worth 3 points)
(simple interest and arithmetic sequences mc)

an auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?

60
93
102
110

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Explicit Formula" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Explicit Formula" ] } ## Identify the sequence parameters $$ \begin{aligned} a_1 &= 30 \ a_2 &= 38 \ a_3 &= 46 \ d &= 38 - 30 = 8 \end{aligned} $$ ## Apply the explicit formula $$ \begin{aligned} a_n &= a_1 + (n - 1)d \ a_{10} &= 30 + (10 - 1) \times 8 \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} a_{10} &= 30 + 9 \times 8 \ a_{10} &= 30 + 72 \ a_{10} &= 102 \end{aligned} $$

60

93

102

110

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the sequence parameters

Apply the explicit formula

Calculate the final value

Answer: